Solving Semi-Open Queuing Networks

A semi-open queuing network (SOQN) is a special type of a queuing network consisting of two parts: an inner network with a population constraint and an external queue to accommodate jobs whose entrance is delayed. We first study an SOQN with a single class of jobs in tandem configuration and then extend our study to multiclass configurations. Multiclass SOQNs fall into two categories: general pallet and dedicated pallet SOQNs. For the general pallet case, we aggregate all classes and solve the resulting single-class SOQN. For the dedicated pallet case, we construct a method based on an existing product-form approximation method for general, multiclass closed networks. Our approximation method combines the matrix-geometric method with the decomposition-aggregation approach. Numerical results show that our approximations have desirable accuracy and efficiency.